The indefinite integral of 1/(x^3-1) with respect to x.
In input form, put into Mathematica 8:
Integrate[1/(x^3 - 1), x]
Gives result:
-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + (1/3)*Log[1 - x] - (1/6)*
Log[1 + x + x^2]
Computing online with the Wolfram integrator:
http://integrals.wolfram.com/index.jsp?expr=1%2F%28x^3-1%29&random=false
Gives:
-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[-1 + x]/3 - Log[1 + x +
x^2]/6
Look at the (1/3)*Log[1-x] term.
Mathematica 8 gives me Log[1-x], the online integrator gives the
answer Log[x-1].
The answers are exactly the same in all other terms. I ran across this
because I was trying the tutorials, and I noticed my answer was
different than the result in the tutorial even.
Is this an error?
Thanks all!